It is: 1,000,000
729, cube of 9 and square of 27
27
729
729
1
6
· it has 2 digits · it is a square number (8 x 8 = 64) · it is a cube number (4 x 4 x 4 = 64)
I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.
The number 64 is equal to ±8 squared and 4 cubed.
26
4
"Taking a cube" is the same basic procedure, whether it's a one-digit number, a three digit number, a complex number, a square matrix, or anything else you can multiply. Taking the cube simply means, multiply the number by itself, in such a way that it appears three times as a factor. For example, if your three-digit number is 235, you calculate the cube as 235 x 235 x 235.